Small Wave Number Region Research Articles

The Oblique Alfvén Ion Beam Instability in the Earth's Ion Foreshock

How ions evolve in the Earth’s ion foreshock is a basic problem in the heliosphere community, and the ion beam instability is usually proposed to be one major mechanism affecting the ion dynamics therein. This work will perform comprehensive analyses of the oblique ion beam instability in the Earth’s ion foreshock. We show that in addition to two well-known parallel instabilities (i.e., the parallel fast-magnetosonic whistler instability and the parallel Alfvén ion cyclotron instability), the oblique Alfvén ion beam (OA/IB) instability can also be triggered by free energy relating to the relative drift dV between the solar wind proton and reflected proton populations. For slow dV (e.g., dV ≲ 2.2V A , where V A denotes the Alfvén speed), it only triggers the OA/IB instability. When dV ≳ 2.2V A , the growth rate in the OA/IB instability can be about 0.6 times the maximum growth rate in parallel instabilities. Moreover, this work finds the existence of two types of OA/IB instabilities. The first one appears at slow dV and in the small wavenumber region at fast dV, and this instability can be described by the cold fluid model. The second one arises in large wavenumber regions at fast dV, and this instability only appears in warm plasmas. Furthermore, through the energy transfer rate method, we propose that the OA/IB instability is driven by the competition among the Landau and cyclotron wave-particle interactions of beam protons, the cyclotron wave-particle interaction of core protons, and the Landau wave-particle interaction of electrons. Because oblique waves can experience significant damping, the importance of the OA/IB instability may be the effective heating of ions in the Earth’s foreshock.

A family of edge-sharing bi-octahedral diruthenium(III,III) compounds containing Ru-Ru single bonds.

From paddlewheel starting reactants Ru2(R'CO2)4+, a family of edge-sharing bi-octahedral (ESBO) diruthenium(III,III) compounds has been prepared, formulated as Ru2(μ-O2CR')2(μ-OR)2(η-L)2 (1-10) [R' = CH3, R = CH3, L = acac (1), tfac (2); R' = CH3, R = CH2CH3, L = hfac (3); R' = CH2CH3, R = CH3, L = acac (4), tfac (5); R' = CH2CH3, R = CH2CH3, L = hfac (6); R' = CH2Cl, R = CH3, L = tfac (7); R' = CH2Cl, R = CH2CH3, L = hfac (8); R' = C6H5, R = CH3, L = tfac (9); and R' = H, R = CH3, L = acac (10); here, acac, tfac and hfac represent acetylacetone, trifluoroacetylacetone and hexafluoroacetylacetone, respectively]. Compounds 1-10 have a similar ESBO coordination geometry of the Ru(μ-O2CR')2(μ-OR)2Ru core with a Ru-Ru center chelated and bridged by two μ-O2CR' and two μ-OR in a trans manner, and each Ru center is also coordinated with a η2-L bidentate ligand. The Ru-Ru distances fall in the range of 2.4560(9)-2.4771(4) Å. The investigation of the electronic spectra and vibrational frequencies as well as theoretical studies with density functional theory (DFT) reveal that compounds 1-10 are ESBO bimetallic species of d5-d5 valence electron counts showing a σ2π2δ2δ*2π*2 electronic configuration. Varying -CH3 to -CF3 groups on the η2-L bidentate ligands coordinating to the Ru(μ-O2CR')2(μ-OR)2Ru core, and according to Raman spectrum measurements combined with theoretical calculations, the intense bands of compounds 1-10 appearing at ∼345 cm-1 in the small-wavenumber region can be assigned to the stretching of the Ru-Ru single bond.

The onset of penetrative convection in a three-layered porous–air–porous system with internal heat source

The study is devoted to a linear stability problem for a system of two horizontal porous sublayers separated by an air interlayer under the influence of the gravity field. The porous sublayers are capable of generating heat with a constant volumetric strength of heat source proportional to the solid volume fraction. Equal temperatures are maintained at the external boundaries of the three-layered system. The onset value for internal convection is numerically determined in the limiting case of a thin air sublayer. The critical wave number is also found, upon reaching which the equilibrium stability is lost in the system, and convective patterns begin to arise. The influence on the convective stability of the ratio of the permeabilities of the layers, the relative thickness of the lower porous sublayer, and the parameter of the air interlayer is analyzed. This parameter is the ratio of the air sublayer thickness raised to the third power to the Darcy number. New results are obtained that take into account the localization of the convective flow. It is shown that the permeability ratio can both destabilize and stabilize the motionless state. An increase in the interlayer parameter unambiguously reduces the convection onset value. A map for the local and large-scale convective regimes has been constructed in the coordinates of permeability ratio versus the air interlayer parameter. A demarcation line of the transition from one regime to another on the map corresponds to the parameters at which the critical internal Rayleigh–Darcy numbers for the two minima of the bimodal neutral curve have equal values. One of the minima belongs to the region of small wave numbers (a long-wave minimum) and defines the onset value for large-scale convection, and the other one is in the region of large wave numbers (a short-wave minimum) and indicates the onset value for local convection. It is shown that with an increase in the air interlayer parameter, the ratio of permeability required for a transition from large-scale to local convective regimes decreases.

Chromous carbonates containing a square-grid layer of {Cr2(CO3)4}n4n- based on a dichromium(II,II) paddlewheel core.

Polymeric coordination compounds based on Cr2n+ paddle-wheel building blocks with non-carboxylate O,O-donor ligands chelating and bridging the Cr-Cr centers have been underexplored hitherto. This paper reports the synthesis and crystal structure of a new homo-valent chromium(ii,ii) compound, Na3HCr2(CO3)4·10H2O (1). It has a two-dimensional structure in which the paddlewheel chromium(ii,ii) units of Cr2(CO3)44- are cross-linked through the carbonate groups. The layers are stacked along the [100] direction, and Na ions fill the intra and interlayer spaces with a neighboring layer distance of about 11.3 Å. The investigation of the primary magnetic properties and theoretical studies with density functional theory (DFT) reveal the partial paramagnetic properties of compound 1 arising from the Boltzmann distribution between a ground state σ2π4δ2 with S = 0 and a low-lying excited state σ2π4δδ* with S = 1 for the Cr2(ii,ii) dimer. According to Raman spectra measurements combined with theoretical calculations, the two Raman bands in the small-wavenumber region at 335 and 297 cm-1 were assigned to the vibration of the Cr-O bonds and the band at 371 cm-1 was assigned to the stretching of the Cr-Cr quadruple bond.

Active Modes and Dynamical Balances in MRI Turbulence of Keplerian Disks with a Net Vertical Magnetic Field

Abstract We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier ( -)space, we identified three types of active modes that define the turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled “the vital area” and are (i) the channel mode, uniform in the disk plane with the smallest vertical wavenumber; (ii) the zonal flow mode, azimuthally and vertically uniform with the smallest radial wavenumber; and (iii) the rest (parasitic) modes. The rest modes comprise those harmonics in the vital area whose energies reach more than 50% of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes; however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by the interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist of disk flow nonmodality modified classical MRI with a net vertical field. The main nonlinear process is the transfer of modes over wavevector angles in Fourier space—the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.

Anti-Langmuir decay instability in Langmuir decay instability cascade

Backward stimulated Raman scattering (BSRS) with Langmuir decay instability (LDI) and anti-Langmuir decay instability (ALDI or anti-LDI) has been researched by Vlasov simulation. The decay productions of anti-LDI in LDI cascade and their evolution with time are demonstrated for the first time. The BSRS reflectivity will be decreased largely through LDI cascade and ALDI in the small wave-number region. Different mechanisms to saturate BSRS in CH (or H) and C plasmas have been demonstrated. The dominant saturation mechanism of BSRS in CH (or H) plasmas is LDI cascade and ALDI. However, in C plasmas, due to very weak Landau damping of ion acoustic waves, LDI cascade will promote stimulated Brillouin scattering (SBS) excitation, then SBS will compete with BSRS and saturate BSRS in the later stage. The proportion of the hot electrons is decreased largely through LDI cascade and ALDI. These results give an effective mechanism to suppress BSRS and hot electron generation in the small wave-number region, which are of important significance in the inertial confinement fusion.

Study of the Transition from MRI to Magnetic Turbulence via Parasitic Instability by a High-order MHD Simulation Code

Abstract Magnetic turbulence in accretion disks under ideal magnetohydrodynamic (MHD) conditions is expected to be driven by the magneto-rotational instability (MRI) followed by secondary parasitic instabilities. We develop a three-dimensional ideal MHD code that can accurately resolve turbulent structures, and carry out simulations with a net vertical magnetic field in a local shearing box disk model to investigate the role of parasitic instabilities in the formation process of magnetic turbulence. Our simulations reveal that a highly anisotropic Kelvin–Helmholtz (K–H) mode parasitic instability evolves just before the first peak in turbulent stress and then breaks large-scale shear flows created by MRI. The wavenumber of the enhanced parasitic instability is larger than the theoretical estimate, because the shear flow layers sometimes become thinner than those assumed in the linear analysis. We also find that interaction between antiparallel vortices caused by the K–H mode parasitic instability induces small-scale waves that break the shear flows. On the other hand, at repeated peaks in the nonlinear phase, anisotropic wavenumber spectra are observed only in the small wavenumber region and isotropic waves dominate at large wavenumbers unlike for the first peak. Restructured channel flows due to MRI at the peaks in nonlinear phase seem to be collapsed by the advection of small-scale shear structures into the restructured flow and resultant mixing.

Acoustic equations for a gas stream in rigid-body rotation

The classical topic of wave propagation in a rotating gas is revisited by deducing scalar wave equations for propagation of acoustic and rotational waves through a plug flow of gas in rigid-body rotation with arbitrary intensities of the radial stratification. In the light of these novel equations, wave propagation is analyzed in two different base gas states: isothermal and homentropic. In both cases, previous findings are recovered that assess the validity of the equations and new results are established. In the non-homentropic but isothermal case, the set of governing equations is reduced to two coupled scalar wave equations with space dependent coefficients for the disturbances of density and pressure. Travelling wave solutions with variable amplitude have been obtained in the limit of weak stratification both for inertial waves as for acoustic waves which, in general, propagate on different frequency bands that overlap in the small wavenumber region. Furthermore, the entropy stratification in the base state is stable and compels the propagation of internal waves, leading to hybrid acoustic-inertial-vortical modes. In the homentropic case, the adiabatic relation between pressure and density disturbances allows to reduce further the governing equations to a single fourth-order scalar wave equation. In this case, the sound propagation velocity depends on the distance to the rotation axis and solutions are found by multiple-scale analyses in the form of waves with slowly varying amplitude and wavenumber. The corresponding eikonal equation shows that acoustic rays are refracted towards the rotation axis, propagating and spinning along and around it. In that way, the swirling gas behaves as an axial waveguide trapping inside any acoustic ray propagating in the vortex with large enough azimuthal and/or vertical wavenumber component.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region.

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number kλ_{De} is small, such as kλ_{De}=0.1, the fluid NFS dominates in the total NFS and will reach as large as nearly 15% when the wave amplitude |eϕ/T_{e}|∼0.1, which indicates that in the condition of small kλ_{De}, the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

Collisional effects on the modulational instability of intense laser pulses in magnetoactive plasmas

AbstractThe modulational instability associated with propagation of an intense laser pulse through a transversely magnetized plasma is investigated in the presence of collisional effects. The source-dependent expansion method for analyzing the wave equation is employed. The dispersion relation is obtained and modulational instability and its growth rate are studied. It is shown that in the absence of collisional effects the modulational instability is restricted to the small wavenumber region and the constant magnetic field reduces the growth rate of the instability. In contrast, in the collisional plasma, there is no upper limit of wavenumber for the existence of modulational instability. In addition, in this case, the growth rate of instability increases as the collision frequency goes up.

Directed Assembly of Block Copolymers by Sparsely Patterned Substrates

Self-consistent field theory and dissipative particle dynamics simulations are used to demonstrate the controlled positioning and alignment of cylindrical domains by chemical surface patterns in an asymmetric slit. Self-assembly of the copolymer melt is simulated near dense and sparse surface patterns, both with one and two characteristic length scales. In particular, we compare the effect of a hexagonal pattern, sparse rectangular pattern, and triangle pattern. The parallel alignment of microdomains between preferentially attractive homogeneous surfaces is shown to transform into the stable perpendicular hexagonal phase in the case of the substrate patterns, which commensurate with the hexagonal morphology in the bulk. For the sparse rectangular pattern, when two different length scales of interactions are involved, and for the sparse hexagonal pattern, we observe that the self-assembly of diblocks multiplies the density of the surface patterns by a factor of 2 and 4, respectively. A 2-fold resolution enhancement was found for sparse triangle pattern with two characteristic length scales. The analysis of the circularly averaged structure factor allowed us to distinguish the structure orientation in a film. Additional peak in the region of small lateral wave numbers is attributed to undulational deformations of cylinder domains under preferable film boundaries. This theoretical work serves to rationalize modern nanolithographic fabrication of high-spatial-frequency arrays using lower-spatial-frequency templates.

Strong scintillation spectra behind the atmosphere with large- and small-scale inhomogeneities

The numerical examination of 2D spectra of strong stellar scintillations observed through the Earth’s atmosphere from space is carried out. The atmosphere contains a combination of statistically independent, anisotropic large-scale and isotropic small-scale inhomogeneities of the refractive index. 2D spectra and vertical and horizontal 1D spectra calculated using them are presented. It is shown that the strong scintillation spectra are not equal to the sum of the spectra formed by separate, statistically independent components. The combination of large- and small-scale inhomogeneities results in a greater dispersion of scintillations in comparison with the absence of latter ones. However, the presence of this combination can lead both to an increase and decrease of dispersion in comparison with the sum of dispersions of the anisotropic and isotropic components depending on their intensity relation. The new effect in 1D horizontal spectra behavior is found in the region of small wave numbers; i.e., the presence of small-scale atmospheric inhomogeneities results in the suppression of spectral power of scintillation formed by only an anisotropic component.

Effects of the Unburned-Gas Temperature and Lewis Number on the Intrinsic Instability of High-Temperature Premixed Flames

The effects of the unburned-gas temperature and Lewis number on the intrinsic instability of high-temperature premixed flames under the constant-enthalpy conditions were investigated by two-dimensional unsteady calculations of reactive flows. A sinusoidal disturbance with sufficiently small amplitude was superimposed on a planar flame to obtain the relation between the growth rate and wave number, i.e. the dispersion relation. As the unburned-gas temperature became higher, the growth rate increased and the unstable range widened. This was due to the increase of the burning velocity of a planar flame. In addition, the obtained numerical results were consistent with the theoretical solutions in small wave-number region. As the Lewis number became smaller ( larger ), the growth rate increased ( decreased ) and the unstable range widened ( narrowed ), which was due to diffusive-thermal effects. The dispersion relation yielded the linearly most unstable wave number, i.e. the critical wave number. The critical wave number increased as the unburned-gas temperature became higher. Thus, the critical wavelength shrank, and then the cell size shrank. To clarify the characteristics of cellular flames induced by intrinsic instability, a finite disturbance with the critical wavelength was superimposed. The superimposed disturbance evolved, and a cellular-shaped front formed. In all Lewis numbers, the behavior of cellular flames became milder as the unburned-gas temperature became higher, even though the growth rate increased. The normalized burning velocities of cellular flames decreased monotonously. This was because that the thermal-expansion effects became weaker owing to the decrease of the difference in temperature between the burned and unburned gases, which was generated by the conditions of constant enthalpy, i.e. constant burned-gas temperature.

Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal

Thermal expansion of two-dimensional itinerant nearly ferromagnetic metal is investigated according to the recent theoretical development of magneto-volume effect for the three-dimensional weak ferromagnets. We particularly focus on the T2-linear thermal expansion of magnetic origin at low temperatures, so far disregarded by conventional theories. As the effect of thermal spin fluctuations we have found that the T-linear thermal expansion coefficient shows strong enhancement by assuming the double Lorentzian form of the non-interacting dynamical susceptibility justified in the small wave-number and low frequency region. It grows faster in proportional to y-1/2 as we approach the magnetic instability point than two-dimensional nearly antiferromagnetic metals with ln(1/ys) dependence, where y and ys are the inverses of the reduced uniform and staggered magnetic susceptibilities, respectively. Our result is consistent with the Grüneisen's relation between the thermal expansion coefficient and the specific heat at low temperatures. In 2-dimensional electron gas we find that the thermal expansion coefficient is divergent with a finite y when the higher order term of non-interacting dynamical susceptibility is taken into account.

Static and dynamic structure and the atomic dynamics of liquid Ge from first-principles molecular-dynamics simulations

The first-principles molecular-dynamics simulation was performed for liquid Ge at $1253\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by using two kinds of simulation cells: The cubic cell of 64 atoms and the rectangular parallelepiped one of 128 atoms. The rectangular parallelepiped cell of 128 atoms was adopted to obtain the dynamic structure factor of liquid Ge in the small wave number region. The long simulation time was adopted, i.e., $66\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the cubic cell and $75\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for the rectangular parallelepiped one. The present first-principles molecular-dynamics simulation reproduces well the experimental static structure factor and radial distribution function. A broad peak around $100\ifmmode^\circ\else\textdegree\fi{}$ in the obtained bond angle distribution function implies the existence of the tetrahedral atomic unit in liquid Ge. The self-diffusion coefficient for the rectangular parallelepiped cell is 20% larger than that of the cubic one. The obtained dynamic structure factor agrees well with the experimental one obtained by the inelastic x-ray scattering experiment [Hosokawa et al., Phys. Rev. B 63, 134205 (2001)], which shows the ``de Gennes narrowing'' of the main peak and the existence of the side peaks. These side peaks represent a longitudinal vibrational motion, which was also supported by the subsidiary peak around $30\phantom{\rule{0.3em}{0ex}}{\mathrm{ps}}^{\ensuremath{-}1}$ in the spectral density of the velocity autocorrelation function. The gradient of the dispersion relation in the present simulation agrees well with the experimental sound velocity. This ``no positive dispersion'' accords well with the inelastic x-ray scattering experiment of Hosokawa et al. The reason for this ``no positive dispersion'' for liquid Ge is discussed in particular concern with its low kinematic viscosity. Though the velocity autocorrelation function itself does not show a cage effect, a microscopic cage effect can be found by the detailed analysis for the trace and environment of the single atomic motion. The atomic movement as a group of 3--5 atoms seems to be present in liquid Ge in addition to individual atomic motions. The covalent bond seems to be also present at least instantaneously in liquid Ge.

Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow

The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.

A large-scale molecular dynamics study of dynamic structure factor and dispersion relation of acoustic mode in liquid and supercritical water

Large-scale and long-time molecular dynamics calculations have been performed using a fluctuating charge model TIP4P-FQ in order to investigate structure and dynamics of supercritical water near the critical point. The calculated Ornstein–Zernike behavior of the structure factor S ( k ) in the small wave number region was in satisfactory agreement with experiment. The intermediate scattering function F ( k , t ) showed much slower decay in the supercritical water than that found in the ambient water. Further, the calculated dynamic structure factor S ( k , ω ) clearly showed the existence of acoustic mode for both systems. The calculated dispersion relation for the liquid water is in good agreement with the IXS data. In the supercritical water near the critical point, the acoustic excitation propagates with a speed of about 420 m/s.

Higher order approximations in reductive perturbation method: strongly dispersive waves

Contribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed early by us. It is shown that the lowest order term in the expansion is governed by the nonlinear Schrödinger equation while the second-order term is governed by the linear Schrödinger equation. For the small wave number region a set of solution is presented for the evolution equations.

Contribution of Higher Order Terms in Nonlinear Ion-Acoustic Waves: Strongly Dispersive Case

Contribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed by us [J. Phys. Soc. Jpn. 68 (1999) 1833]. In the analysis it is shown that the lowest order term in the expansion is governed by the nonlinear Schrodinger equation while the second order term is governed by the linear Schrodinger equation. For the small wave number region a set of solution is presented for the evolution equations.

Dispersion and damping of a two-dimensional plasmon in a metallic surface-state band.

We have studied, for the first time, the energy and the linewidth dispersion of a plasmon in a dense two-dimensional electron system in a metallic surface-state band on a silicon surface. As expected from the considerably high effective density and long Fermi wavelength of the system, the plasmon energy dispersion exhibited an excellent agreement with the nearly free-electron theory. However, in a small wave number region below the Landau edge, we have observed an anomalous linewidth dispersion which nearly free-electron theories do not predict.